Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
num=int(input())
def check(n):
    if(n==0):
        return False
    x=1+(8*n)
    
    sq=math.sqrt(x)
    
    qwe=int(sq)
    
    if(qwe*qwe==x):
         return True
    return False
flag=0
for i in range(1,(num//2)+1):
    i=(i*(i+1))//2
    
    if((num-i)<0):
        break
    if(check(num-i)):
            flag=-1
            print("YES")
            break
    
if(flag==0):
         print("NO")